Variable coupling transformers



ug. 8, 959 I R. w. mpp 2,9oo,612

VARIABLE COUPLING TRANSFORMERS 2 Sheets-Sheet 1 Filed Sept. 26, l955INVENTOR' Rober? W. Trip`p ATTORNEYS Aug. 18, 1959 R. w. TRIPP 2,900,612

VARIABLE COUPLING TRANSFORMERS Filed Sept. ze, 1955 2 Sheets-Sheet 2INVENTOR.

Robert W. Tripp BY f 1.,BM

ATTORNEYS United States Patent Office 2,900,61Z Patented Aug. 18, 19592,900,612 VARIABLE COUPLING TRANSFORMERS Robert W. Tripp, Bronxvlle,N.Y., assignor, by nene assignments, to Inductosyn Corporation, CarsonCty, Nev., a corporation of N evada Application September 26, 1955,Serial No. 536,464 24 Claims. (Cl. 336-123) This invention relates totransformers of adjustable coupling factor. The invention providestransformers of this type in which the coupling factor or factors areaccurately known and preferably sinusoidal functions of the relativeposition of two relatively rotatable elements which bear the primary andsecondary windings of the transformer. The transformers of the inventionpreferably include no ferromagnetic material and depend upon inductivecoupling between closely spaced primary and secondary windngs. Thewindings are of spiral or of spiral and other arcuate shape, mounted(usually on fiat disks of insulating material) for relative rotation ina common axis which is coaxial with the axis of the spiral or otherarcuate patterns to which the windings conform. The transformers of theinvention are useful as synchros for .angular data measurement andtransmission, and especially as computing elements for the generation ofvoltages which represent circular functions of angular displacementsbetween primary and secondary members. In particular the transformers ofthe invention find application as resolvers which can be constructed tooperate with high accuracy.

The invention will now be further described in conjunction with theaccompanying drawings in which:

Fig. 1 is a plan view of one transformer member (which may be either aprimary or a secondary) according to the invention;

Fig. 2 is a plan view of a member similar to that of Fig. 1 but havingtwo separate windings in space quadrature, the windings of both Figs. 1and 2 being spiral in shape;

Fig. 3 is a plan View of another transformer member according to theinvention hearing a single circularly arcuate sectoral winding;

Fig. 4 is a plan View of still another transformer member according tothe invention including two windings of circularly arcuate sectorialshape in space quadrature, the two windings of the member of Fig. 4being subdivided into sections positioned and dimensioned in order toirnprove the sinusoidal quality of the coupling functions between eachof them and the winding or windings of a primary member according toFig. 1 or Fig. 2 when a member according to Fig. 4 is combined with amember according to Fig. 1 or Fig. 2 into a complete transformer;

Fig. 5 is a view in side elevation of a complete transfomer according toone embodiment of the invention; and

Fig. 6 is a view in side elevation of another complete transformeraccording to the invention.

One form of transformer .according to the invention is shown in Fig. 5.It includes two disks 2 and 4 made of non-ferromagnetic insulatingmaterial, for example glass, mounted for relative rotation in an axis 6.Either or both of the disks 2 and 4 may be rotatable with respect to thesurrounding frame of reference; it is sufficiert that the disks berotatable with respect to each other. The disk 2' is shown mounted on ashaft 8 and the disk 4 is shown mounted on a shaft 10. Of course thedisks 2 and 4 need not be round in shape; the outline of the disks isimmateral, although they are advantageously round and centered on theaxis of relative rotation. The disks have faces 12 and 14 which areplane and perpendcular to the axis of relative rotation 6. The disk ordisks movably mounted must be restrained against relative axiatl motionso that the spacing between the faces 12 and 14 will remain constantwithin reasonably close tolerances. These tolerances may for example beof the order of a few thousandths of an inch in a nominal disk spacingwhich may for example be of the same order of magnitude as theseparation of adjacent convolutions of the spiral conductors which, aswill presently be described, are provided on one or both disks. The diskspacing may however also be substantially smaller. In Fig. S the disk 2and its shaft 8, to which the disk 2 is aflixed, are shown as mountedfor rotation at bearings 16 which include a thrust surface to preventendwise play of the disk 2.

The faces 12 and 14 bear each one or more windings of the typesillustrated in Figs. 1-4, at least one face hearing a winding of one ofthe types illustrated in Figs. l and 2, and the coupling factor orcoefficient between each winding of one disk 2' and each winding of theother disk 4 varies with the angular positional relation of the disksabout their axis 6. In preferred embodiments of the invention thewindings are so .arranged that this coeflicient is sinusoidal, goingthrough one cycle per relative revolution of the disks.

In the transformers of the nvention, there may be one or more primarywindings and one or more secondary windings, all primary windings (ifplural) being fixed with respect to each other and all secondarywindings (if plural) being fixed with respect to` each other, allprimary windings being movable as a unit With respect to all secondarywindngs. Either winding or group of windings so fixed with respect toall other windings may serve as the primary or as the secondary windingor windings of the transformer and the terms rotor and stator, ifdesired, may be interchangeably applied to either of such groups ofrelatively fixed windings and to the support therefor. Hereinafter theterm member will be applied to any one of such groups of windings of atransformer, together with the support or supports therefor.

Transformer members according to the invention will now be described infurther detail with reference to Figs. 1-4.

Fig. 1 illustrates one form of transformer member according to theinvention including a single winding. in Fig. 1 a disk 18 ofnon-ferromagretic and non-conducting material such as glass is providedwith a plane face 20 on which there is arranged a conducting 'windinggeuerally iudicated at 22. The winding 22 comprises two interlacedspirals 23 and 25 of equal and constant pitch, concentric in a point 24.Each of the spirals includes at least one complete turn and preferablyincludes a number of complete turns, five or six turns being a practicalminimum in the preferred embodiments of the invention in whichsinusoidal coupling functions of rotor-stator angle are to be obtaincd.In the assembled transformer the member of Fig. 1 -is mounted with point24 on the axis of relative rotation of the transformer members and withthe face 20 perpendicular to that axis. Point 24 may be referred to asthe center or axis of the member, and the two spirals 23 and 25 areequiangularly disposed with respect to it, i.e. they are spaced apart byof a circle around the point 24.

In the embodinent of Fig. l the inner ends of the two spirals areconnected together and the winding 22 which they form may be fed atterminals 26 and 28 at the radially outer ends thereof. The two halvesof the winding may instead be connected in series at their outer ends,the connection being made in either case so that in adjacentconvolutions of the two spirals current fiows in opposite directions,clockwise in one and counterclockwise in the other. The double spiralwinding 22 so formed may be provided by photoetching of a sensitizedsilver surface deposited on the face 20 of the disk.

A simple form of transformer according to the invention comprises twomembers of the type illustrated in Fig. l, mounted as illustrated inFig. 5 with the windings on the adjacent faces of the two disks as somounted. In such a case the spiral patterns of both primary andsecondary windings should, when viewed in any one direction along theaxis 6, be of the same sense. for example as so viewed counterclockwiserotation about the axis 6 along all spirals should result in motionradially outward from, or inward to, the axis. Moreover all of thespirals should have the same pitch.

If the two ends of the double spiral winding of one member are energizedwith a suitable alternating voltage for example in the upper range ofaudio frequencies, the magnitude of the alternating voltage induced intothe winding of the other member will then be a function of the relativeangular position of the two members in their axis 6 of relative rotation(Fig. 5). Slip rings may be provided on the rotating member or membersfor connection to the ends of the winding. Alternatively rotarytransformers may be employed for this purpose, or even fiexible leads ifcontinuous rotation need not be provided for.

As the relative position of the primary and secondary members ischanged, the coupling factor changes also, passing through 360 of acycle for one complete revolution in relative position. The coefcient ofcoupling or coupling factor will not for this simple structure be ingeneral a sinusoidal function of angle, but that it will be a cyclicalfunction is clear from consideration of the fact that there are tworelative positions 180 apart for the two members (the disks 2 and 4, interms of Fig. 5) in which the windings of the two members will be atequal and minimum separations. In these positions of maximum couplingthe two double spiral windings Will lie on a common spiral cylindricalsurface coaxial in the axis 6 of Fig. 5. One of these positions is theposition of maximum couplng in one sense while the other is the positionof maximum coupling in the other sense. The positions 90 from those ofmaximum couplng will be at least approxirnately positions of minimumcoupling.

The tr ansformers of the invention find advantageous application asresolvers, employing two windings on at least the secondary member. Insuch resolvers a sinusoidal input voltage or voltages to one member, theprimary, are resolved in the secondary member into sinusoidal voltageswhose amplitudes represent the sine and cosine of the angle betweenprimary and secondary members, measured from an arbitrary zero relativeposition of reference for which the amplitude in one secondary windingis zero (sine voltage) and for which the amplitude in the othersecondary 'winding is a maximum (cosine voltage). A transformeraccording to the invention constituting a resolver requires in itssecondary two windings whose coupling waves with respect to the primaryshall be 90 out of phase. That is to say, the rotor-stator position forwhich the coupling wave from each primary winding to one secondarywinding is at a maximum is the rotor-stator position for which thecoupling wave from that primary winding to the other secondary windingis a minimum. A combination of two windings so oriented with respect toeach other as to provide coupling waves so dephased is illustrated inFg. 2. In Fig. 2, a disk 30, which may be identical with disk 18 of Fig.1, beats two double spiral windings 32 and 34, each one of which may beidentical with the winding 2.2 shown in Fig. 1. The winding 32 isdisplaced with respect to the winding 34 by 90 about the center point 36in which both windings are concentric. In the embodiment illustrated,the windings 32 and 34 Thiis 4 i have a cross-over point in the vicinityof the center 36. This may be provided by means of an insulating bridgeor foil 38 laid down over a short length of one winding before the otherwinding is applied. Alternatively the radially outer ends of the twospirals forming each winding may be connected together, as in theembodiment of Fig. 1, by conductors on the outer periphery or back faceof the disk.

An elementary form of resolver according to the invention may beprovided by combining a member according to Fg. l with a memberaccording to Fig. 2 in the physical relation of Fig. 5. If two inputvoltages are to be provided for, both members may be of the typeillustrated in Fig. 2.

In transformers according to the invention either the primary orsecondary member will include a winding or windings of the double spiraltype illustrated in Fig. l. While the other member may include a windingor windings of the same type, other forms of winding in which theoperative portions are circular arcs may be preferred, since this makesit possible to place the leads to the two members in such position thatthey do not have inductive coupling between them to introduce unwantedharmonics or other Components into the coupling waves. In addition,division of the winding or windings of one member into sectoral sectionsas will presently be described permits incorporation of a number offeatures which eilect harmonic cancellation and balance for wobble anddecente-ring of the disk supports of the windings.

Transformer members according to the invention employing such arcuatewindings are shown in Fgs. 3 and 4. Thus in Fig. 3 disk 40 bears asingle winding generally indicated at 42 having terminals 44 and 4-6 anda plurality of inductively effective portions conforming to arcs ofcircles concentric in a center point 48 which, in the assembledtransformer embodying the member of Fig. 3 and a member according toFig. l or Fig. 2, lies on the axis of relative rotation. The arcuateportions are joined together in series by radial portions whichterminate in leads to the terminuals 44 and 46. The winding 42 includesa plurality of circularly arcuate portions 51-56, concentric in point48, centered in angular extent on a common radius from the point 48, andradially spaced from each other by one-half the pitch of either of thespiral portions of the double spiral winding or windings of the othertransformer member, for convenience called the primary.

For more complete symmetry it is advantageous to position the radialleads between the successive arcuate portions 51--56 symmetrically withrespect to the length of those arcuate portions themselves so that, asindicated in Fig. 3, each of the portions S-56 has associzted therewithan equal portion 51' 56' of the same radius and arcuate length, arrangedto conduct in the same clockwise or counterclockwise sense as its matingportion. Hereinafter reference -to the arcuate portions Sit- 56 will beunderstood to refer to -the sum of the portions 51 and 51', 52 and 52',etc. lt is however possible to locate the radial leads at one end of thearcuate portions,

one radial lead being continuous.

There must be in the secondary' winding 42 at least one arcuate portion,and there are preferably several of them, six or eight for example, thenumber of spiral convolutions in the winding or windings of the primarymember being sutlicient so that each spiral extends preferably at leastone complete turn beyond the outcrmost and beyond the innermost of thearcuate portions of the secondary member in order to minimizc the efeetof inhomogeneities in the field adjacent the inner and outer ends of thespirals of the primary.

The angular extent of the arcuate portions of such a winding as isillustrated in Fig. 3 may be chosen within rather wide limits. Inpreferred embodiments of the invention this angular extent will berather small, of the order of 60, as will be explained presently. Allarcuate portions centered on a common radius are preferably ofequiangular extent about their common center of curvature. So longhowever as the angular extent of the arcuate portions is less than 360there will for all but two relative positions of the primary andsecondary members and for any given exctation of a primary winding beinduced in each arcuate portion of the secondary a net voltage, i.e. thecoupling factor Will not be zero. The coupling factor of any one arcuateportion of the winding of Fig. 3 to any one winding of a primary beraccording to Fig. 1 or Fig. 2 will have a maximum of one sign when,approximately, the mid-point of that portion is at its nearest approachto one of the spirals of the primary winding under consideration, andthe coupling factor will have its maximum value of opposite sign at therelative position 180 from that just considered. Since the pitch of thearcuate portions s one-half that of the spiral windings of the primarymernber and since successive arcuate portions of the secondary winding42 are series connected so` that radially successive portions thereofearly current in opposite directions, clockwise and counterclockwiseabout the axis, the voltages induced in all of the arcuate portions add.lt is clear that the coupling Wave between the series-connected portions51-56 and one of the double spiral windings of the member of Fig. 2 willbe 90 displaced in phase from the coupling wave between those portionsand the other 'double spiral winding of the primary according to Fi 2.

%u Fig. 3 the complete winding 42 includes not only the arcuate portions51-56 but a duplicate set of arcuate portions 61-66 positioned 'l80 fromthe first. The portions 61-66 are connected together in series inexactly the same way as are the portions SEF-5%, each set of arcsforming what may be called a section of the winding 42. In Fig. 3 thefirs -t section is identified by the reference character 5'9 while thesecond section is identified by the reference character 69. Since thecoupling waves between any one rotor winding (either of the windings 32and 34 of Fig. 2.) and the section 59 is 18G displaced from the couplingwave between the same rotor winding and the section 69, reenforcemen tof the coupling waves to the two sections of the secondary winding ofFig. 3 is obtained by crossing `on or near the axis the radial-conductors by which the two sections are connected in series. Alongwith other advantages to be described presently, provision of twoseries-connected sections in the winding 42 obviously increases themagnitude of the coupling factor, which is low in maximum value even atbest.

In general, the coupling Wave or waves observed with :the transformersof the invention as thus far described, are not accurately sinus'oidal.Appreciable harmonic content may be expected to be present even if theinevitable departures of the winding patterns from perfect geometry,decentering thereof and wobble due to nonperpendicularity of the diskfaces in the transformer axis were removed. The harmonics present in thecoupling waves are primarly of odd order since the symmetry of themembers makes the coupling waves symmetric about their maximum andminimum: values.

In their preferred embodiments the transformers of the invention andhence the members of which those transformers are made include featuresof Construction in the dimensioning and disposition of the windingswhich minmize harmonics in the coupling waves. The member of Fig. 3incorporates one form of harmonic compensation according to theinvention. In the embodiment of Fig. 3 the third harmonic of thecoupling wave to the single winding of that figure is minimized byemploying in that member arcuate portions of l20 angular extent. Bymaking the sections 59 and 69 120 in extent each, each arcuate portionin each section extends over one-third of the radial cycle of each ofthe windings in the primary member according to Fig. l or Fig. 2. Eachsuch arcuate portion therefore extends over a whole cycle of the thrdharmonic in the coupling wave between 'either primary winding and thatarcuate portion. consequently for all rotor-stator positions in atransformer including a member according to Fig. 3, the sum of thevoltages induced instantaneously in any arcuate portion of the windingof Fig. 3 includes all phases of any third harmonic in the couplingwave, and the third harmonc in the coupling wave to each such arcuateportion is therefore zero. More generally, cancellation of any desiredharmonic may be obtained by the use of sections including' circularlyarcuate portions concentric in the transforner axis whose angularextent, expressed as a fraction of 360, is the reciprocal of the orderof the harmonic to be sup-pressed. Thus the fifth harmonic may besuppressed by sectors of 72 angular extent. When arcuate windings of thetype illustrated in Fig. 3 are employed, with or' without harmonicsuppression, it is desirable to provide two diametrcally oppositeseries-connected sectors as illustrated in Fig. 3. This not onlyimproves the coupling factor but eifects compensation for decentering ofthe center 48 from the axis of rotaton When the member according to Fig.3 is combined with a .primary member into relatively rotatable relationin a transformer. Provision of diametrically opposite sectors alsocompensates at least partially for wobble, i.e. non-perpendicularity ofthe plane of the disk 40 to that axis. Provision of such diametricallyopposite sectors is however not necessary. Transformers according to theinvention analogous to the usual self-synchronous motors and generatorsmay be provided from a single winding rotor according to Fig. 1 and athree-phase stator including three equiargularly disposed separatesecondary sectoral arcuate winding similar to the sectors 59 and 69 ofFig. 3.

The embodiment of Fig. 3 includes only a single winding, and even if thesecond section of that winding were suppressed the extent of the firstsection 59 would preclude the provision of another separate winding ofthe same shape in space quadrature with the first without overlapping.Hence other winding patterns are desirable for embodiments of theinvention such as resolvers in which it is desired to have two windingsin space quadrature on both members of the transformer. Fig. 4illustrates a transformer member according to the invention suitable foruse with a member according to Fig. 2 to provide such a transformer withtwo primary and two secondary windings.

On the member of Fig. 4 there are provided two windings in spacequadrature, and these windings are subdivided into sections which aredimensioned and located with respect to each other in such a fashion asto compensate for the third and tw'elfth harmonics in the coupling wavesand also to compensate for wobblng and decentering errors. The member ofFig. 4 includes a disk '76 intended to be mounted for rotation in anaxis perpendicular to the face of the disk seen in the figure. '72identifies the point on the disk face on which the conductor patternsare concentric. There are provided on the disk eight conducting patternsor winding sections 73 80, all of the same general type as the sections59 and 69 of Fig. 3. All of the sections are of 30 angular extent, andsuccessive sections are centered on radii which are alternately 60 and30 apart, so that two sections centered on radii 60 apart are providedin each quadrant of the disk face. Each of the sections includes aplurality of circularly arcuate portionsconcentric in the center 72.Each section has two terminals, at the perphery of the disk in Fig. 4.The sections are there connected together in series in two groups toform two windings in space quadrature. The sections 73 and 74 fallwithin one quadrant of the disk face and together with the sections 77and 78 in the diametrically opposite quadrant form one of the twoquadrature windings.` Provision of radially opposite symmetric windingsections effects cancellation of wobble and decentering errors as in theembodiment of Fig. 3. Moreover the sections 73 and 74 are symmetricrespectively in two radii R and R' of the disk face, apart. consequentlythe third harmonic Component of the coupling wave between any primarywinding and the section 73 is half of a third harmonic cycle displacedin phase from the third harmonic component of the coupling wave betweenthe same primary winding and the section 74. Accordingly cancellation ofthe third harmonic may be eiected by connecting sections 73 and 74 inseries, and similarly cancellation of the third harmonic may be obtainedbetween sections '7'7 and 78. In order that the sections 73 and 74 besymmetric in the radii R and R' and yet together occupy no more than onequadrant of the disk face, as is necessary if two separate but identicalwindings are to be provided in space quadrature without overlapping, thesections 73 and 74 (and also sections 75-88) are limited to 30 ofangular extent. A 30 angular dimension for these sections providescompensation of the twelfth harmonic of the coupling waves by virtue ofthe same effect as that which in the member of Fig. 3 is operative toprovide third harmonic compensation.

The series connection of sections 73 and 74 is, as indicated by theexternal lead 81, such as to give reenforcement between the fundamentalComponent of the coupling waves to each of these sections.

The same precaution is observed in the series interconnection ofsections 77 and 78 in the opposite quadrant as is indicated by lead 82.In connecting together in series sections 73, 74 on the one hand and 77,78 on the other, a reversal is made by means of leads 83 and 84 becauseof the l phase difference between the fundamental Component of thecoupling wave from any primary winding to a secondary in one quadrantand the fundamental Component of the coupling wave from that primary toa secondary winding in the opposite quadrant. The first winding of thetransformer member of Fig. 4, comprising sections 73, 74, 77, 78, isgenerally indicated by the reference character 90, and possesses twoterminals 92 and 94 in lead 84. in a similar manner leads --88interconnect sections 75, 76 and 79, 80 into a single series circuit todevelop the second winding of the transformer member of Fig. 4,generally indicated at 96 and having terminals 98 and 10th. The leads'interconnecting the sections 73-80 have been indicated diagrammatically only. They may be placed on the peripheral edge or backface of the disk.

When harmonic compensation is eitected as in the member of Fig. 4 withrespect to the third harmonic by series interconnection of twocircumferential ly displaced sectoral winding sections to form a windingor part of a winding, there is a diflerence in phase between the fun-`damental Components of the separate coupling waves between any windingof the other transformer member and those sections. Consequently, thecoupling wave `for the two sections in series together is different inphase from the coupling in either section alone and has an amplitudegiven by the vector sum of the amplitudes ot the separate coupling wavesto each section. The senarate coupling waves reinforce each other,however, since their phase difference is less than Further suppressionof harmonics may be achieved by a suitable dimensioning of the width ofthe conductors with respect to the space between immediately adjacenfgeometrically parallel series-connected portions thereof which carry thesame current in opposite directions, in accordance with the disclosureand claims of the copend ing application Serial No. 509,168, now PatentNo. 2,799,835, assigned to the assignee hereof, filed May 13, 1955. Thismethod of harmonic suppression is applicable separately to transformermembers according'to Figs. 1 and 2, which members have windingsincluding spiral portions of one complete revolution or more, and alsoto members of the type illustrated in Figs. 3 and 4, which members havearcuate windings of lesser angular extent. Any one harmonic may becanceled in a transformer made up of members of these types byapplication of this technique to one of the two transformer members.Another harmonic may be canceled by application of the technique to theother transformer member.

According to this technique as applied to the member of Fig. 1 forexample, the third harmonic may be eliminated by making the width of theconductors of the one double spiral winding in that member twice thespace between radially adjacent portions of that winding, i.e., betweenadjacent portions of the individual spiral conductors 23 and 25, so thatthe conductor width will be two thirds of the cycle comprising oneconductor and the space which separates it from an adjacent conductorcarrying the same current in the opposite direction. As applied tomembers of the type illustrated in Figs. 3 and 4, elimination of thethird harmonic by this technique requires that the width of the arcuateconductors be two thircls of the cycle comprising each such arcuateconductor and the space which separates it from. an adjacent arcuateconductor, which carries the same current in the opposite direction. Ina transformer including a member according to Fig. 2, the third harmoniccannot be eliminated by applying this technique to such a member becauseof the presence of two double spiral windings interlaced with each otherand carrying different currents. The fifth harmonic may, however, beeliminated on such a member by making the width of each conductor twofifths of the cycle comprising one conductor and the space whichseparates it from the radially adjacent conductor of the same winding,i.e., that which carries the same current but in the opposite direction.The three fifths of the cycle not occupied by the conductor of onewinding leave room for a similarly dimensioned conductor of the otherwinding. Of course, this same criterion may be applied to a singlewinding member according to Fig. 1, or to members of the type of Pigs. 3and 4, in order to suppress the fifth harmonic.

Transformers according to the invention satisfactory for angular datatransmission of the type effected with self-synchronous motors andgenerators do not require sinusoidal coupling waves. The transformers ofthe invention however find application as resolvers in computingapparatus in which it is desirable that the absolute magnitudes of thevoltages induced by the primary winding or windings into the secondariesbe individually sine and cosine functions of rotor-stator angle. Inorder to achieve this result it is necessary not only to suppressharmonics in the coupling waves but to maintain constant the axialspacing between primary and secondary members, to variations in whichthe coupling 'factor is sensitive, or else compensation must be providedfor variations in coupling function due to variations ii; that spacing.

To this end applicant has provided as a presently preferred embodimentof his invention a transformer as illustrated in Fig. 6, designed toserve as a resolver with two input windings in quadrature and two outputwindings in quadrature. The transformoi' of Fig. 6 comprises a shaft 11@on which is mounted a rotor disk 112, of insulating material as before,and two stator members or disks 114- and lilo likewise of insulatingmaterial. The shaft 110, which passes through central apertures in disks114 and 116, is mounted in bearings 118 and 120 to define an axis ofrevolution 122 for the rotor, with which the shaft and rotor disk aredimensioned and fitted to rotate concentrically as nearly aspracticable, with the faces of the rotor and stator disks perpendicularto this axis. The bearings 113 and 1263 inoreover include a thrustelement to limit within reasonably close tolerances play of the rotor112 lengthwise of the axis 122.

The rotor disk 112 advantageously bears on each of its faces .two doublespiral windings as illustrated in Fig. 2, and each stator disk bears twoarcuate windings as illustrated in Fig. 4. The four rotor windings arecombined in pairs and .the four stator windings are also combined inpairs to provide 'for the resolver two resolver wndngs in spacequadrature ?fixed with respect to the shaft 110 and two resolverwindings in space quadrature fixed with respect to the frame ofreference in which the stator disks are mounted. Each of these pairs ofstator windings includes one winding froni disk 114 and one from disk116., and each of these pairs of rotor windings includes a winding fromeach face of the rotor disk 112, disk 112 providing in substance twotransformer members according to Fig. 2 and each of stator disks 114 and116 providing a transformer member according to Fig. 4.-

The two halves of each such resolver winding may be connected in seriesor in parallel with each other. In

the case of a resolver winding serving as a primary, it is desirablethat the two halves thereof be connected in series with each other inorder that the same current flow through both.

The spiral windings according to Fig. 2 on the two faces of the rotordisk 112 may be of the same or opposite hand, a suitable selection ofend points of the eight wndings (in the sense of the windings of Figs. 2and 4) for interconnection by pairs into the four resolver windingspermitting in either event the achievement of reinforcement of thecoupling waves ohtained.

The resolver of Fig. 6 will exhibit coupling functions which areindependent of the small amount of end play of the rotor shaft whichmust be allowed for in the manufacture of a mechanical device, since thedecrease in coupling between one pair of rotor and stator resolverwindings upon endwse motion of the rotor in one direction will bebalanced by an increase in coupling between the other pair of resolverwindings.

The resolver of Fig. 6 may incorporate any and all of the features ofconstruction for compensation of harmon'ics and of wobble anddecentering errors which have been discussed hereinabove. By comparisonwith a transformer according to Fig. 5, a transformer according to Fig.6 provides an additional possibility for harmonic compensation in theresulting combined coupling waves in the same manner essentially as thatdescribed in connection with Fig. 4. Thus if the spiral patterns on thetwo faces of disk 112 are phased together, i.e. similarly positionedabout the axis 112 and if the conducting patterns on disks 114 and 116are displaced from each other by 60 about the aXis 122, the fundamentalComponents of the coupling waves attributable one to each half of theresolver as a whole will be 60 apart, and upon conibination of these twowaves cancellation of the third harmonic in the resultant over-allcoupling wave will be etfected. This is not, however, the principaladvantage to be obtained from the use of a transformer according to Fig.6 in place of one according to Fig. 5.

In one design of a resolver according to Fig. 6 the double spiralwindings from both faces of the disk 112 combined in pairs to providetwo resolver windings were so chosen that each such pair included twowindings 90 apart, and a similar choice was made in combining the fourstator windings of the type shown in Fig. 4 in pairs to form the twostationary resolver windings, in order to help balance residual elfectsof wobble, decentering, and aXial displacement of the rotor on theabsolute value of the coupling between rotor and stator.

The invention has been described hereinabove in terms of presentlypreferred embodiments thereof. Various changes and departures from theparticular structures which have been described may however be madewithin the scope of the invention. For example, the transformer membersof Figs. 3 and 4 have been described as having windings comprising arcsof circles concentric with the axis of rotation of the transformers inwhich the mem bers are to be employed. Transformers according to theinvention may however be constructed with members of the general typeillustrated in Figs. 3 and 4 but in which the arcs are arcs of spiralsrather than circles, or arcs of circles not individually concentric inthe intended aXis of rotation of the member. The essential property forthe achievement of harmonic compensation according to the methoddescribed in connection with Fig. 3 is that of the two conductors ininductive relationship, one (for convenience here assumed to be theseconday) should include a portion having a spiral pitch not identicalin amount and sign to the pitch of the conductor which is of the spiraltype illustrated in Fig. 1 (for convenience here assumed to be theprimary). The circularly arcuate conductors of Figs. 3 and 4- may beregarded as spirals of Zero pitch. With such non-identity of pitch thesecondary conductor may be dimensioned and positioned to span a simplefraction of one cycle of the spiral magnetic field of the primarymember, such fraction being an integral number of multiples of `thereciprocal of the order of the harmonic in the coupling wave sought tobe suppressed. It will be understood that on the primary member eachpair of radially adjacent series-connected spiral conductors carryingthe same current in opposite directions will generate (if energized) aspiral field having one spiral pole of each polarity. When as in Figs. land 2 the two series-connected spiral conductors are l apart, there aretwo such fields or half fields interlaced back to back and or" equalradial dimensions. These two spiral fields may be thought of asconstituting a single fully cyclical spiral field, the spatial polecycle of which eX- tends from a pole of one sign opposite one spiralconductor to a pole of the same sign opposite the adjacent convolutionof the same spiral conductor, i.e. the radially adjacent conductorcarrying the same current in the same direction. The spiral pitch ofthis cyclic magnetic field is therefore, in the embodiments illustratedin Figs. 1 and 2, equal to the geometrical pitch of the spiralconductors which give rise to it. Therefore in transformers including amember as illustrated in Fig. l or 2, for compensation according to theprinciple illustrated in Fig. 3, the ends of the inductively effectiveportions of the secondary conductors thereof (as distinguished from theradial connecting portions, in the embodiments of Figs. 3 and 4 forexample) should have as their points of nearest approach in the plane ofthe primary winding or windings points which in that plane differ in thephase of the primary conductor pitch cycle by a simple fraction as abovedefined. Of course also, in order to be inductively effective, :theseportions of the secondary should have a component of length parallel tothe length of the primary.

With the inductively active portions of the secondary windings takingthe form of circular arcs concentric of the transformer aXis as in Figs.3 and 4, and with the twospiral winding members of Figs. l and 2, theangle subtended by these arcs on that axis is the same fraction of 360as is the fraction of the conductor pitch cycle on the primary windingcovered by those arcs individually, so that compensation according tothe method illustrated in Fig. 3 is obtained with such circular arcs bygiving to them an angular extent which is the same fraction of 360 asthe reciprocal of the order of the harmonic to be suppressed. However,if spiral arcs or circular arcs not so concentric in the transformeraxis are enployed, it is possible to compensate for a harmonic of anygiven order with arcs which subtend at the axis of the transformer asmaller or larger angle than that dened by the fraction of 360 which isequal to the reciprocal of the order of the harmonic in question.Indeed, suitable spiraling of the arcs of the secondary member permitsaveraging, and hence compensation, for any desired harmonic with anygiven angular eXtent for the stator sectors subtended at the transformeraXis. Circularly arcuate secondary 11 windings have primarily theadvantage of ease in generation of the master patterns therefor.

Also, in the description of Figs. 3 and 4, it has been stated that theradial separation of successive arcuate portions is constant, and thatthe Plural sections connected together, such as sections 59 and 69 ofFig. 3 or '33 and 74 of Fig. 4, are identical and identically placed.These conditions need not be Strictly fulfillcd in the transformers ofthe invention, and indeed it may be desirable to make intentionaldepartures therefrom.

In said copending application Serial No. 5053168, filed May 18, 1955,and assigned to the assignee hereof, there are described transformers ofother types in which both primary and secondary members include a verylarge number of poles, as contrasted with the relatively small number ofpoles in the transformers of the present appli cation, the member ofFig. l, for example, exhibiting along any radius one north and one southpole for each passage of either of the spirals 23 and 25 across thatradius. Of course, the polarity of these poles is reversed in time withevery half cycle of the excitation signal. In the transformers of saidcopending application last referred to suppression of the harmonics inthe coupling wave is eiected by a variation, either lumped orcontinuous, in the pole pitch of one winding by comparison with the polepitch or" another winding with which the first is in inductive relation,one of these being a primary and the other a secondary. Possiblysuppression of harmonics might be undertaken in the transformers of thepresent invention by the same or similar methods. Thus in a memberaccording to Fig. 3 of the present application, the radial separation ofsuccessive arcuate conductors in the section 59 might be made slightlydifferent from one half the pitch of the spirals of the winding orwindings of the associated member or members according to Pig. l or 2with which the modified member according to Fig. 3 was to be used, thismodification in relative pitch of the two members being such that thetotal ingredient of a given harmonic induced in the section 59 would addto zero. The variation in length of the arcuate conductors of thesection 59 would theoretically, however, suggest a nonlinear change inpitch relationship between the primary and secondary' members withradius, which might be tliflicult to execute.

Somewhat similarly, the two series-connected sections 59 and 69 of Fig.3 might be located at unequal distances from the center 48 in order toposition them at unlike phases of a selected harmonic in the pitch cycleof the primary of a member according to Fig. l or Fig. 2. Here also,however, since the effective area of a section varics with its radiallocation, a proper selection of such displaced radial positions appearsto be diicult.

Also, compensation according to Fig. 3 and the modifications thereofwhich have been described may be achieved, on members such as those ofFigs. 3 and 4, with respect to any given harmonic by means of arcuateconductors which spari, on the other transformer member of the Fig. 1 or2 type, fractons of the pitch cycle of the spiral windings of the lattermember amounting to an integral number of cycles of the harmonic inquestion even though this integral number is greater than one. Thus inthe embodiment of Fig. 3 itself, while each of the circular arcs 51--56and 61-66 subtends 120 and therefore spans, on a transformer memberaccording to Fig. 1 or Fig. 2 to be associated with a member accordingto Fig. 3, one third of the spiral pitch cycle of either of the windingsof Fig. 2 and hence a single cycle of the third harmonic in the couplingwaves, 'each of those arcs also spans two complete cycles of the sixthharmonic, three cycles of the ninth and so on, providing compensation asto these other harmonics as well.

In the preferred embodiments of the invention which have been describedherein, the coupling wave or waves between the two transformoi' membersgo through one complete cycle per revolution of the members with respectto each other in their axis of relative rotation. This is due to thenature of the spiral windings illustrated in Figs. 1 and 2, each ofthese windings including two series-connected spirals displaced fromeach other by l about the center of the disk face on which they areprovided. With such a pattern one revolution of the disk exposes apoint, conceived as fixed in a plane adjacent the plane of such awinding, to one complete cycle of positions relative to such a doublespiral winding.

The invention is not however limited to such structures. Transformersaccording to the invention can be constructed with any desired number ofcoupling cycles per revolution. For example, starting with a givenmember according to Fig. 3 or 4, a transformer having three couplingcycles per revolution may be produced by providing a spiral memberhaving six equiangularly spaced spiral conductors whose spiral pitch issix times the radial separation of adjacent arcuate conductors on themember according to Fig. 3 or 4. Adjacent inner ends of the spirals arethen connected together in pairs, and adjacent outer ends are alsoconnected together in pairs to produce a six-spiral winding. If a secondwinding in quadrature is to be provided on the spiral member, its sixspiral conductors are arranged half way between the spirals of the firstwinding so that the member will bear in all twelve spiral conductors 30apart about the center of the disk. In general, a transformer withcycles for its coupling waves per revolution of the transformer membersmay be provided by means of a spiral member having, for each windingthereon, Zu equiangularly disposed spiral conductors connected inseries. lndeed a transformer according to the invention can beconstructed to operate over a portion of one revolution in relativeposition of its members with a spiral member having a pluralty of spiralconductors which (if, as will usually be desirable, more than two areprovided) are spaced from each other by equal angular intervals aboutthe disk center but which do not cover the whole face of the disk, forexample if the angular separation of adjacent spirals is incommensurablein 360. With all of these constructions the coupling wave from eachspiral winding of the spiral member to each winding of the other memberwill go through 180 of phase for a relative rotation of the twotransformer members equal to the angular spacing of two adjacentseries-connected spiral conductors in each winding of the spiral member.

In all, the geometrical pitch of the spiral conductors should be suchthat, in an angular advance on the spiral member equal to that overwhich the coupling wave is to go through 360, the radius of the spiralswill change by the spacing center to center of three arcuate conductorsin one of the sectoral sections on the member of the transformeraccording to Fig. 3 or 4, i.e. by two arcuate conductor intervals. Thusin a transformer having one cycle per revolution the pitch of the spiralconductors, eg. those shown in Figs. 1 and 2, is such that the radius ofeach spiral changes by two arcuate conductor intervals in 360geometrical degrees of advance. Similarly in a transformer having forits coupling waves two cycles per revolution and therefore havingseries-connected spiral conductors 9G apart (preferably four of them) ineach winding of its spiral member, the pitch of the spiral conductors issuch that the radius of each spiral advances by two arcuate conductorintervals in 180 geometrical degrees of advance. i

With transformers having more than one eoupling cycle per revolution,the dimensioning a'nd/ or disposition of the arcuate conductors on thetransformer member according to Fig. 3 or 4 should be appropriatelyaltered it harmonic compcnsation is to be obtained by the meansdescribed in connection with those figures.

It has been stated that, for compensation according to the method ofFig. 3, the ends of each arcuate conductor should have as their pointsof nearest approach to the plane of the spiral member points which inthat plane,

and at their respective circumferential positions, diifer in the phaseof the spiral magnetic field of the primary member by a fraction of theradial length of that magnetic field equal to the reciprocal of theorder of the harmonic to be suppressed (or by a multiple of thatfraction). With circularly arcuate conductors as illustrated in Fig. 3this means for a transformer having one coupling cycle per revolutionthat the arcuate conductors in the member according to Fig. 3 shouldsubtend at the center of the disk on which they are mounted an angleequal to the fraction of 360 whose reciprocal is the order of theharmonic to be suppressed.

With respect to the additional compensation illustrated in Fig. 4, thetwo series-connected sectoral sections between which compensation iselfected are centered on bearings which are spaced by an angle equal tothe angle over which the phase of the harmonic Component in the couplingwave which is to be suppressed changes by l80.

With transformers according `to the invention in which the coupling wavegoes through 360 of phase for a lesser number of dcgrees of rotation thecorresponding dimen-- sions of the arcuate conductors on the memberaccording to Fig. 3 or 4 must be proportionally reduced. If thetransforner has two coupling wave cycles per revolution and includes amember according to Fig. 3, including circularly arcuate conductorsconcentric with the axis of disk rotation, the arcuate extent of thesearcuate conductors should be reduced by a factor of two, Likewise in amember according to Fig. 4 for use in such a trans-' fonner having twocoupling wave cycles per revolution;

the angular separation of the series-connected sectoral sectors shouldbe reduced by a factor of two. It will be remembered that in such atransformer the spirals are twice as steep, for the same pitch of thearcuate conductors, as in a transformer having one coupling wave cycleper revolution. Hence the phase of the spiral magnetic fields changestwice as fast with angle around the center of the disk.

More generally stated, for compensation of harmonics in the couplingwave according to the principles described hereinabove in connectionwith Fig. 3 but in transformers having a number 'of coupling wave cyclesper revolution other than one, the points in the plane of the spiralmember nearest the ends of the .arcuate conductors employed for suchcompensation should diifer in the phase of the geornetrical pitch cycleof the spiral conductors on the primary member by a fraction which isrelated to the harmonic to be suppressed as hereinabove explained inconnection With transfo'mers having one coupling wave cycle perrevolution except that in the transformers now under consideration thenumber of coupling wave cycles per revolution appears as a factor in thedenominator of that fraction. Indeed this number always so appears, thefactor being unity for transformers having one coupling wave cycle perrevolution. The same principles apply to the provision of compensationaccording to the method illustrated in Fig. 4, in transformers having anumber of coupling wave cycles per revolution other than unity. 1

In similar fashion the angular separation of two windings on any onetransformer member which are to be in space quadrature is inverselyproportional to the number of coupling wave cycles per revolution,quadrature meaning quadrature of the angular interval over which thecoupling wave goes through one cycle. Thus if the transformer includeson its spiral member 211 equiangularly disposed spiral conductors in onewinding so as to have 360/ n cycles in its coupling waves per relativerevolution of the transformer members, the angular separation on eithermember of two windings which are to be in space quadrature should be360/4n.

I claim:

1. A transforner comprising two members having each a plane face, meansto support said members with their said faces parallel to each other forrelative rotation in an axis perpendicular to said faces, two spiralconductors of equal and constant pitch disposed on one of said facescoaxially of said axis, said conductors being connected in series atradially sinilarly positioned ends thereof, and a conductor disposed onthe other of said faces, said last-named conductor including a portionconforming to an a'c of a curve coaXial of said axis.

2. A transformer comprising two supports having each a plane face, meansto support said supports with their said faces parallel to each otherfor relative rotation in an aXis perpendicular to said faces, two spiralconductors of equal and constant pitch disposed on one of said facescoaxially of said axis, said conductors being connected in series atradially similarly positioned ends thereof, and a conductor disposed onthe other of said faces, said last-named conductor including a portionconforming to an arc of a spiral coaxial of said axis.

3. A transformer comprising two insulating supports having each a planeface, means to support said supports with their said faces parallel toeach other for relative rotation in an aXis perpendicular to said faces,an even plurality of spiral conductors of the same pitch equiangularlydisposed on one of said faces coaxially of said axis, circumferentiallyadjacent of said conductors being connected in series at radiallysinilarly positioned ends thereof to produce a series winding includingall conductors of said plurality, and a winding disposed on the other ofsaid faces, said last-named winding including a plurality ofseries-connected arcuate conductors equiangularly disposed with respectto each other about said axs.

4. A transformer comprising two insulating supports having each a planeface, means to support said supports with their said faces parallel toeach other for relative rotation in an axis perpendicular to said faces,a plurality of spiral conductors of equal and constant pitch disposed onone of said faces coaxially of said axis, each of said conductors beingspaced from at least one other of said conductors bythe same angularinterval about said axis, said conductors being connected in series atradially similarly positioned ends thereof to form said conductors intoa two-terminal series winding, and a conductor disposed on the other ofsaid faces, said lastnamed conductor including a portion whose ends haveas their points of nearest approach in the plane of said spiralconductors points differing in phase of the pitch cycle of any of saidspiral conductors by a fraction of the pitch of any of said spiralconductors.

5. A transformer comprising two insulating supports having each a planeface, means to support said supports with their said faces parallel toeach other for relative rotation in an aXis perpendicular to said faces,two spiral conductors of the same pitch equiangularly disposed on one ofsaid faces coaxially of said axis, said conductors being connected inseries at radially sinilarly positioned ends thereof, and a conductordisposed on the other of said faces, said last-named conductor includinga portion conforming to a circular arc coaXial with said axis andsubtending at said axis an angle equal to a simple fraction of 360 whosedenominator is a small integer.

6. A transformer comprising two insulating supports having each a planeface, means to support said supports with their said faces parallel toeach other for relative rotation about an axis perpendicular to saidfaces, two spiral conductors of equal and constant pitch equiangularlydisposed on one' of said faces coaxially of said axis, said conductorsbeing connected in series at radially similarly disposed ends thereof,and a winding on the other of said faces, said winding including aplurality of series-connected arcuate portions coaxial in said axis,successive of said portions being radially spaced by onehalf the pitchof said spiral conductors.

7. A transformer comprising two insulating supports having each a planeface, means to support said supports, with their said faces parallel toeach other and with a substantially constant spacing therebetween, forrelative rotation about an axis perpendicular to said faces, two spiralconductors of equal and constant pitch equangularly arranged on one ofsaid faces coaXially of said aXis, said conductors being connected inseries so that radially adjacent convolutions thereof carry current inopposite directions, and a winding on the other of said faces includinga plurality of series-connected circularly arcuate portions coaxial insaid axis, successive of said portions being radially spaced by one-halfthe pitch of said spiral conductors, all of said portions subtending thesame angle at said axis and being centered on a common radus from saidaxis, said angle being a fraction of 360 whose reciprocal is a smallinteger.

8. A transformer comprising first and second insulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and with a substantially constant spacingtherebetween, for relative rotation about an axis perpendicular to saidfaces, two spiral conductors of equal and constant p-itch equi-angularlyarranged on each of said faces coaxially of said aXis, all of saidconductors having' the same pitch, the conductors on each of said facesbeing connected in series so that radially adjacent convolutions thereofcarry current in opposite directions, all of said conductors spiralingin the same sense about said aXis as viewed in one direction along saidaXis.

9. A transformer comprising first and second insulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and with a substantially constant spacingtherebetween, for relative rotation about an axis perpendicular to saidfaces, two spiral conductors of equal and constant pitch equiangularlyarranged on one of said faces coaxially of said axis, said conductorsbeing connected in series so that radially adjacent convolutions thereofCarry current in opposite directions, and two windings arranged on theother of said faces coaxially of said aXis, said lastnamed windingsextending circumferentially of said other face and being disposed inspace quadrature.

10. A transformer comprising first and second insulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and With a substantially constant spacing there-'between, for relative rotaton about an aXis perpendicular to said faces,four spiral conductors of equal and constant pitch equiangularlyarranged on one of said faces coaxially of said aXis, opposite of saidconductors being connected in series at radially sirnilarly disposedends thereof, and a winding on the other of said faces, said wndingincluding a plurality of series-connected arcuate portions coaXial insaid aXis, successive of said portions being radially spaced by one-halfthe pitch of any one of said four spiral conductors.

11. A transformer comprising first and second insulating supports`having each a plane face, means to support said supports, with theirsaid faces parallel to each other and with a substantially constantspacing therebetween, for relative rotation about an aXis perpendicularto said faces, two spiral conductors of equal and constant pitchequiangularly arranged on one of said faces coaxially of said axis, saidconductors being connected in series at radially similarly disposed endsthereof, and a winding on the other of said faces having twoseriesconnected parts, each of said parts including a plurality ofseries-connected `arcuate portions radially spaced by substantiallyone-half the pitch of either of said spiral conductors, the saidportions of each of said parts extending circumferent-ially of saidsecond face symmetrically about a common radius, said radii beingseparated by a simple fraction of 360 having small integers as numeratorand denominator.

12. A transformer comprising first and second insulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and with a substantially constant spacingtherebetween, for relative rotation about an aXis perpendicular to saidfaces, two spiral conductors of equal and constant pitch equi-angularlyarranged on one of said faces coaXially of said ax is, said conductorsbeing connected in series at radially sinilarly disposed ends thereof,and two Windings in space quadrature on said second face, each of saidwindings comprising two series-connected parts, each of said partsincluding a plurality of arcuate portions occupying a sectoral areaabout said axis, the sectoral areas occupied by said series-connectedparts being substantially centered on radii from said aXis separated byan angle which is a simple fraction of '360 having small integers asnumerator and denominator.

13. A transformer comprising three insulating supports, two of saidsupports having each a plane face and the third of said members havingtwo parallel plane faces, means to support said first two supports withtheir faces parallel and at a fixed separaton and to support said thirdsupport between said first two supports for rotation about an axisperpendicular to the faces of said three supports and with asubstantially constant and equal spacing between said third support andeach of said first and second supports, four spiral conductors ofconstant and equal pitch equiangularly arranged on each face of saidthird support, opposite of said conductors on each face of said thirdsupport being connected in series at points thereof substantiallyequidistant from said axis, interconnections between each pair ofseriesconnected conductors on one face of said third support and onepair of series-connected conductors on the other face of said thirdsupport to form two windings having spiral conductors, eight sectoralwindings on each of said first and second support, each of said eightwindings comprising a plurality of series-connected circularly arcuateportions successive ones of which are radially spaced by one-half thepitch of each of said spiral conductors, all of said portions subtendingsubstantially 30 on said axis and all portions of each of said eightwindings being centered on a common radius, successive of said radiibeing alternately 60 and 30 apart, means connecting in series those ofsaid eight windings 60 apart and further connecting in series those ofsaid eight windings l apart to form two windings in space quadrature oneach of said first and second supports, and interconnections betweensaid last-named windings in pairs, each of said pairs including one ofsaid last-named windings from each of said first and second supports.

14. A transformer comprising two insulating supports having each a planeface, means to support said supports with their said faces parallel toeach other for relative rotation in an aXis perpendicular to said faces,two spiral conductors of the same pitch equiangularly disposed on one ofsaid faces coaXially of said axis, said conductors being connected inseries at radially similarly positioned ends thereof, and a plurality ofwindings equiangularly disposed 'on the other of said faces, each ofsaid windings including a plurality of series-connected arcuateportions, successive of said portions being radially spaced by one-halfthe pitch of said spiral conductors.

iS. A transformer comprising first and second insulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and with a substantially constant spacingtherebetween, for relative rotation about an aXis perpendicular to saidfaces, two spiral conductors of equal and constant pitch equiangularlyarranged on one of said faces coaxially of said axis, said conductorsbeing connected in series so that radially adjacent convolutions thereofearry current in opposite directions, and two Windings arranged inspaced quadrature on the other of said faces, said last-named windingsextending circumferentially of said axis.

17 z tr fsrmp & ent ana atai supports having each ,a planefacegneansto,upprt said supports with their said faces parallel to each' other forrelative rotat'onin .an. aXis perpendicular; to said, faces, two spiralc n uc or .of. .th pitch egiangularly disposed. .on

aid id randu tp s being connected in series at radially similarlypositioned ends thereof, and a windng disposed on the other of saidfaces, said windng including two series-connected sections equiangularlydisposed about said axis, each of said sections including a plurality ofseries-connected arcuate portions, successive of said portions beingradially spaced by one-half the pitch of said spiral conductors, all ofsaid portions in any one of said sections subtending the same angle atsaid axis and being centered on a common radius from said ax s.

17. A transformer comprising two insulating supports having each a planeface, means tosupport said supports with their said faces parallel toeach other for relative rotation in an axis perpendicular to said faces,two spiral conductors of the same pitch equiangularly disposed on one ofsaid faces coaxially of said axis, said conductors being connected inseries at radially similarly positioned ends thereof, and two windingsdisposed in space quadrature on the other of said faces, each of saidwindings including two series-connected sections equiangularly disposedabout said axis, each of said sections including a plurality ofseries-connected portions, successive of said portions being radiallyspaced by one-half the pitch of said spiral conductors, all of saidportions in any one of said sections subtendng the `same angle at saidaxs and being centered on acommon radius from said axis.

18. A transformer comprising first and second nsulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and with a substantially constant spacingtherebetween, for relative rotation about an axis perpendicular to saidfaces, four spiral conductors of equal and constant pitch equiangularlyarranged on one of said faces coaxially of said axis, opposite of saidconductors being connected in series at radially smilarly disposed 'endsthereof, and two windings arranged in space quadrature on the other ofsaid faces, each of said windings including two seriesconnectedsections, each of said sections including a plurality ofseries-connected arcuate portions, successive of said portions beingradially spaced by one-half the pitch of said spiral conductors, all ofsaid portions in any one of said sections being centered on a commonradius from said 'axis, the said radii of series-connected ones of saidsections being separated by an angle which is a simple fraction of 360having small integers as numerator and denominator.

19. A transformer comprisng first and second nsulating supports havingeach a plane face, means to support said supports, with their said facesparallel to each other and with a substantially constant spacingtherebetween, for relative rotation about an axis perpendicular to saidfaces, four spiral conductors of equal and constant pitch equiangularlyarranged on one of said faces coaxially of said axis, opposite of saidconductors being connected in series at radially similarly disposed endsthereof, and two windings arranged in space quadrature on the other ofsaid faces, each of said windings including two seriesconnected sectionsdisposed 180 apart about said axis, of said sections including aplurality of series-connected arcuate portions, successive of saidportions being radially spaced by one-half the pitch of said spiralconductors, all of said portions in any one of said sections beingcentered on a common radius from said axis.

20. A transformer comprising two supports having each a plane face,means to support said supports with their faces parallel to each otherfor relative rotation in an axis perpendicular to said faces, a windngdisposed on one of said faces, said windng including a plurality ofarcuate rent in circumferentially opposite directions abgunsaid axis,and a plurality of spiral conductors of equal and constant pitchdisposed on the other of said faces coaxially of said axis, each of saidspiral conductors` being spaced from at least one other of said spiralconductors by the same angular interval about said axis,circumferentially adjacent of said spiral conductors being connected inseries at radially sirnil'arly positioned ends thereof to form saidspiral conductors into a two-terminal series windng.

21. A transformer comprising two supports having each a plane face,means to support said supports with their faces parallel to each otherfor relative rotation in an axis perpendicular to said faces, a windngdisposed on one of said faces, said windng including a plurality ofarcuate conductors extending across a common bearing about said axis,-said arcuate conductors having on said hearing substantially uniformspacing radially from said axis, said arcuate conductors being soconnected in *series that radially adjacent of said arcuate conductorsCarry current in circumferentially opposite directions about said axis,and Zn spiral conductors of equal and constant pitch equiangularlydisposed on the other of said faces coaxially of said axis,circumferentially adjacent of said spiral conductors being connected inseries at radially similarly positioned ends thereof to form said spiralconductors into a two-terminal series windng, the pitch of said spiralconductors being substantially equal to 2n times said spacing, n beingan integer.

22. A transformer comprising two insulating supports having each a planeface, means to support said supports with their said faces parallel toeach other for relative rotation in an axis perpendicular to said faces,2n spiral conductors of equal and constant pitch equiangularly disposedon one of said faces coaxially of said axis, circumferentially adjacentof said conductors being connected in series at radially similarlypositioned ends thereof to form said conductors into a two-terminalseries windng, and a conductor disposed on the other of said faces, saidlast-named conductor including a portion whose ends have as their pointsof nearest approach in the plane of said spiral conductors pointsdiffering in phase of the pitch cycle of any of said spiral conductorsby a simple fraction of the pitch of any of said spiral conductors, nbeing an integer.

23. A transformer comprising two supports having each a plane face,means to support said supports with their faces parallel to each otherfor relative rotation in an axis perpendicular to said faces, aplurality of spiral conductors of equal and constant pitch disposed onone of said faces coaxially of said axis, each of said conductors beingspaced from at least one other of said conductors by the same angularnterval about said axis, circumferentially adjacent of said conductorsbeing connected in series at radially similarly positioned ends thereofto form said conductors into a two-terminal series windng, and aconductor disposed on the other of said faces, said last-named conductorincluding a portion conforming to a circular arc coaxial with said axisand subtending at said aXis an angle equal to a fraction of 360.

24. A transformer comprising first and second nsulating supports havingeach a plane face, means to support said supports with their said facesparallel to each other and with a substantially constant spacngtherebetween for relative rotation in an axis perpendicular to saidfaces, 2n spiral conductors of equal and constant pitch equiangularlydisposed on one of said faces coaxially of said axis, circumferentiallyadjacent of said conductors being connected in series at radially simi-19 larly positioned ends thereof to form a two-terminal References Citedin the file of this patent series Winding, and two Wndings arranged onthe other UNITED STATES PATENTS of said faces coaxially of said axis,said last-named windings extending circumferentially of said axis andhaving 1,134,840 Goldthorp Apr. 6, 1915 their Centers of gravityseparated by 360/4n degrees, n 5 1,610,122 Edenburg Dec. 9, 1926 beingan integer. 2,685,070 Childs July 27, 1954 Patent No. 2,900, 612

,August l8, 1959 Robert W Tripp It is herebj certified that error a ofthe above numbered patent requiring c Patent should read as correctedbelow.

ppears in the-printed specifcation orrecton and that the said Letterscolumn 17,' in' 64, ,after ".axis," insert each Signed and sealed thisl4th day of June 196&

(SEAL) Attest:

KARL H. AXLINE ROBERT C. WATSON Attesting Officer Commissoner of PatentsUNITED STATES PATENT OFFICE CERTIFICATE CORBECTION Patent N o. 2', 900,612

August l 1959 Robert W., Tripp It is herebj Certified that error appearsin theprinted specification of the above numbered patent requiringcorrection and that the said Letters Patent should read as correctedbelow.

column 17 line' 64, 'after' "axis insert each Signed and sealed this14th day 'of June 1960.

(SEAL) Attest:

KARL H. AXLINE Attestng Officer ROBERT C. WATSON Commissioner of Patents

